A central limit theorem for fields of martingale differences

Abstract: We prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result has been known for Bernoulli random fields. Here, only ergodicity of one of generating transformations is supposed.